Problem: Simplify the following expression: $y = \dfrac{9n^2 - 90n + 81}{n - 9} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ y =\dfrac{9(n^2 - 10n + 9)}{n - 9} $ Then we factor the remaining polynomial: $n^2 {-10}n + {9} $ ${-9} {-1} = {-10}$ ${-9} \times {-1} = {9}$ $ (n {-9}) (n {-1}) $ This gives us a factored expression: $\dfrac{9(n {-9}) (n {-1})}{n - 9}$ We can divide the numerator and denominator by $(n + 9)$ on condition that $n \neq 9$ Therefore $y = 9(n - 1); n \neq 9$